Question

A body of mass $5\,kg$ moving with a velocity $10\,m{s^{ - 1}}$ collides with another body of the mass $20\,kg$ at rest and comes to rest. Velocity of the second body due to the collision is:-
A. $2.5\,m{s^{ - 1}}$
B. $5\,m{s^{ - 1}}$
C. $25\,m{s^{ - 1}}$
D. $2\,m{s^{ - 1}}$

Answer 1

Hint: We will use the principle of conservation of linear momentum to answer this problem, and then we will use equations using this principle to ascertain the velocity of the second body following the impact.

Formula used:
The principle of conservation of linear momentum says that Initial momentum of a system is always equal to final momentum of a system.
${P_i} = {P_f}$
where $P = mv$ denotes the momentum of a body defined as the product of mass of the body and the velocity of the body.

Complete step by step solution:
We have given that, the initial conditions of both bodies are ${m_1} = 5kg,{u_1} = 10\,m{s^{ - 1}}$ and ${m_2} = 20kg,{u_2} = 0$ so net initial momentum of the system is,
${P_i} = {m_1}{u_1} + {m_2}{u_2} \\
\Rightarrow {P_i} = 50\,kgm{s^{ - 1}} \\ $
And after the collision first body came to rest which means zero velocity therefore zero momentum and let velocity of second body is v then final momentum of the system is,
${P_f} = {m_2}v \\
\Rightarrow {P_f} = 20v \\ $
Now, using law of conservation of linear momentum we have,
${P_i} = {P_f} \\
\Rightarrow 50 = 20v \\
\therefore v = 2.5\,m{s^{ - 1}}$
Hence, the correct answer is option A.

Note: It should be remembered that, in addition to the law of conservation of momentum, there are two basic conservation laws: the law of conservation of energy, which states that energy is conserved, and the law of conservation of angular momentum in rotational dynamics, which states that the total angular momentum of the system is conserved when no external torque is applied to the body.